An article by Wilkie and Bodenhausen (2015), claimed that people have a feminine association with even numbers, while having a masculine association with odd numbers. Below are the observed data of around 130 (n differs per number) bachelor students, in an attempt to replicate the original findings.
The Bayesian binomial test gives 2 versions of the Bayes factor and prior posterior plot: one for the proportion of "Feminine" responses, and one for the proportion of "Masculine" responses. In correspondence with the original authors' claims (proportion feminine responses > 0.5 for even numbers; proportion masculine responses > 0.5 for odd numbers), we look at the positive Bayes factor (BF+0) for the even numbers, while looking at the positive Bayes factor for the odd numbers. Note that if we would have done a two-sided test (results provided at the end), the Bayes factor (BF10) will be the same for either proportion (masculine/feminine). For each test, we use uninformed prior distribution(beta (a = b = 1).
Based on the Bayes factors below, I would claim that while there is some evidence for a gendered association for some digits, it is not so simple as stating that odd numbers are feminine and even numbers are masculine. Only for the numbers 1 & 2 did we observe very compelling evidence in favor of the theory. For the numbers 0, 3, 7, 9 we observed some degree of evidence in favor of the null (varying from weak to strong evidence). For 4, 5, 6, and 8 we observed some degree of evidence in favor of the theory (varying from weak to strong evidence).
| Level | Counts | Total | Proportion | BF₊₀ | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 | Feminine | 59 | 124 | 0.476 | 0.076 | ||||||
| Masculine | 65 | 124 | 0.524 | 0.182 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 | Feminine | 44 | 128 | 0.344 | 0.023 | ||||||
| Masculine | 84 | 128 | 0.656 | 120.509 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 | Feminine | 84 | 128 | 0.656 | 120.509 | ||||||
| Masculine | 44 | 128 | 0.344 | 0.023 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 | Feminine | 63 | 128 | 0.492 | 0.096 | ||||||
| Masculine | 65 | 128 | 0.508 | 0.127 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 | Feminine | 74 | 126 | 0.587 | 1.469 | ||||||
| Masculine | 52 | 126 | 0.413 | 0.038 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 | Feminine | 47 | 125 | 0.376 | 0.029 | ||||||
| Masculine | 78 | 125 | 0.624 | 10.474 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 | Feminine | 79 | 129 | 0.612 | 5.696 | ||||||
| Masculine | 50 | 129 | 0.388 | 0.031 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 | Feminine | 56 | 127 | 0.441 | 0.049 | ||||||
| Masculine | 71 | 127 | 0.559 | 0.484 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 | Feminine | 77 | 127 | 0.606 | 3.864 | ||||||
| Masculine | 50 | 127 | 0.394 | 0.032 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 | Feminine | 74 | 127 | 0.583 | 1.209 | ||||||
| Masculine | 53 | 127 | 0.417 | 0.039 | |||||||
| Note. For all tests, the alternative hypothesis specifies that the proportion is greater than 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1). | |||||||||||
An interpretation of the Bayes factors, for each of the 10 digits:
In order to get an accurate estimate of the posterior distribution, we can also conduct the two-sided analysis. Generally, for parameter estimation the two-sided model is used (explanation/demonstration here).
| Level | Counts | Total | Proportion | BF₁₀ | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 | Feminine | 59 | 124 | 0.476 | 0.129 | ||||||
| Masculine | 65 | 124 | 0.524 | 0.129 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 | Feminine | 44 | 128 | 0.344 | 60.266 | ||||||
| Masculine | 84 | 128 | 0.656 | 60.266 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 | Feminine | 84 | 128 | 0.656 | 60.266 | ||||||
| Masculine | 44 | 128 | 0.344 | 60.266 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 | Feminine | 63 | 128 | 0.492 | 0.112 | ||||||
| Masculine | 65 | 128 | 0.508 | 0.112 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 | Feminine | 74 | 126 | 0.587 | 0.753 | ||||||
| Masculine | 52 | 126 | 0.413 | 0.753 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 | Feminine | 47 | 125 | 0.376 | 5.251 | ||||||
| Masculine | 78 | 125 | 0.624 | 5.251 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 | Feminine | 79 | 129 | 0.612 | 2.863 | ||||||
| Masculine | 50 | 129 | 0.388 | 2.863 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 | Feminine | 56 | 127 | 0.441 | 0.267 | ||||||
| Masculine | 71 | 127 | 0.559 | 0.267 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 | Feminine | 77 | 127 | 0.606 | 1.948 | ||||||
| Masculine | 50 | 127 | 0.394 | 1.948 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 | Feminine | 74 | 127 | 0.583 | 0.624 | ||||||
| Masculine | 53 | 127 | 0.417 | 0.624 | |||||||
| Note. Proportions tested against value: 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1). | |||||||||||